Intermediate Algebra Tutorial 41


Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 41: Rationalizing Denominators and Numerators
of Radical Expressions



WTAMU > Virtual Math Lab > Intermediate Algebra > Tutorial 41: Rationalizing Den and Num of Radical Expressions


 

checkAnswer/Discussion to 1a

problem 1a
 

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.

 
Since we have a square root in the denominator,  we need to multiply by the square root of an expression that will give us a perfect square under the square root in the denominator. 

So in this case, we can accomplish this by multiplying top and bottom by the square root of 11:
 

ad1a1

*Mult. num. and den. by sq. root of 11
 
 

*Den. now has a perfect square under sq. root
 
 

Step 2: Make sure all radicals are simplified

AND

Step 3: Simplify the fraction if needed.
  

ad1a2

 
 
 

*Sq. root of 121 is 11
 

 
 

(return to problem 1a)

 


 

checkAnswer/Discussion to 2a

problem 2a
 

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the numerator.

 
Since we have a cube root in the numerator,  we need to multiply by the cube root of an expression that will give us a perfect cube under the cube root in the numerator. 

So in this case, we can accomplish this by multiplying top and bottom by the cube root of ad2a1:
 

ad2a2

 

*Mult. num. and den. by cube root of ad2a1
 
 

*Num. now has a perfect cube under cube root

 
 

Step 2: Make sure all radicals are simplified

AND

Step 3: Simplify the fraction if needed.
  

ad2a3

 

*Cube root of 125 y cubed is 5y

 
 

(return to problem 2a)

 


 

checkAnswer/Discussion to 3a

problem 3a
 

Step 1: Find the conjugate of the denominator.

 
In general the conjugate of a + b is a - b and vice versa.

So what would the conjugate of our denominator be?

It looks like the conjugate is ad3a1.
 

Step 2: Multiply the numerator and the denominator of the fraction by the conjugate found in Step 1 .

 
ad3a2

*Mult. num. and den. by conjugate of den.
*Product of the sum and diff. of two terms
 
 

 
 

Step 3: Make sure all radicals are simplified

AND

Step 4: Simplify the fraction if needed.
 

No simplifying can be done on this problem so the final answer is:

ad3a3
 

(return to problem 3a)

 

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WTAMU > Virtual Math Lab >Intermediate Algebra >Tutorial 41: Rationalizing Den and Num of Radical Expressions


Last revised on July 21, 2011 by Kim Seward.
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